Answer:
[tex]V = \left[\begin{array}{ccc}5&-1\end{array}\right][/tex]
Step-by-step explanation:
We want to reflect this 2x1 vector on the line y = x.
To make this reflection we must use the following matrix:
[tex]R=\left[\begin{array}{cc}0&1\\1&0\\\end{array}\right][/tex]
Where R is known as the reflection matrix on the line x = y
Now perform the product of the vector <-1,5> x R.
[tex]\left[\begin{array}{ccc}-1\\5\end{array}\right]x\left[\begin{array}{ccc}0&1\\1&0\end{array}\right]\\\\\\\left[\begin{array}{ccc}-1(0) +5(1)&-1(1)+5(0)\end{array}\right]\\\\\\\left[\begin{array}{ccc}5&-1\end{array}\right][/tex]
The vector matrix that represents the reflection of the vector <-1,5> across the line x = y is:
[tex]V = \left[\begin{array}{ccc}5&-1\end{array}\right][/tex]
